Rapid thermal emittance and quantum efficiency mapping of a cesium telluride cathode in an rf photoinjector using multiple laser beamlets

Thermal emittance and quantum efficiency (QE) are key figures of merit of photocathodes, and their uniformity is critical to high-performance photoinjectors. Several QE mapping technologies have been successfully developed; however, there is still a dearth of information on thermal emittance maps. This is because of the extremely time-consuming procedure to gather measurements by scanning a small beam across the cathode with fine steps. To simplify the mapping procedure, and to reduce the time required to take measurements, we propose a new method that requires only a single scan of the solenoid current to simultaneously obtain thermal emittance and QE distribution by using a pattern beam with multiple beamlets. In this paper, its feasibility has been confirmed by both beam dynamics simulation and theoretical analysis. The method has been successfully demonstrated in a proof-of-principle experiment using an L-band radiofrequency photoinjector with a cesium telluride cathode. In the experiment, seven beamlets were generated from a microlens array system and their corresponding thermal emittance and QE varied from 0.93 to 1.14 $\mu$m/mm and from 4.6 to 8.7%, respectively. We also discuss the limitations and future improvements of the method in this paper.


I. INTRODUCTION
Beam brightness is a key figure of merit for photoinjectors, and its continuous improvements in the past few decades have enabled the success of a lot of acceleratorbased machines such as: X-ray free electron laser [1,2], electron-positron linear collider [3,4], ultrafast electron diffraction and microscopy [5,6], Thomson scattering Xray source [7,8], etc. With the further development of the above machines, higher requirements are imposed on both the peak and the average brightness of the electron beam. While the peak brightness depends mainly on the beam emittance, especially the thermal emittance of the photocathode, the average brightness depends on the quantum efficiency (QE) of the photocathode due to the limitation of the average laser power. Therefore, further improvements of the thermal emittance and QE of the photocathodes are very desirable.
Further developments of the photocathode put higher requirements on the accurate photocathode diagnosis. The measurements of the thermal emittance and QE are becoming a subject of intense investigation [9][10][11][12], among which the mapping characteristics of the photocathode, i.e., the variations across the cathode surface, are of great significance. In the past few years numerous efforts have been spent on the QE mapping measurements with different methods, such as photoemission electron microscope [13], digital micromirror device [14], raster scanning a focused laser spot across the cathode surface [15], and cathode imaging [16]. The results of these QE mappings demonstrate different QEs at different locations on the cathode. Similarly as the QE, the thermal emittance should be different at different locations on the cathode, and a thermal emittance mapping should be of similar significance of the QE mapping. However, the mapping * dych@mail.tsinghua.edu.cn of the thermal emittance has not been reported until yet. The laser diameter employed in the thermal emittance measurement is usually larger than 1 mm [17], and the measured emittance can be regarded as a weighted average over the illuminated area, with the weighting determined by the transverse intensity profile of the emitted electron beam.
The thermal emittance and QE may vary across the cathode surface due to the local surface roughness, local contaminants and/or stoichiometry, and a mapping measurement of the thermal emittance and QE can reveal the variation of the photoemission, and offer flexibility in choosing the emission site for laser illumination. In this paper, we propose a new method to measure the thermal emittance map. A pair of microlens arrays (MLAs) [18] were employed to redistribute the laser beam to produce a periodic transverse pattern, consisting of a two-dimensional array of beamlets, and the laser pattern beam was then illuminated to a cesium telluride photocathode to produce an electron pattern beam. The electron beamsizes of all beamlets were monitored on a downstream YAG screen with the change of the solenoid strength. The thermal emittance was measured with a solenoid scan technique. The thermal emittances of all beamlets (thermal emittance mapping) can be achieved by only a one-time solenoid scan. This paper is organized as follows. Section II introduces the beamline layout employed in the experiment and the laser pattern beam production with MLAs. The overlap problem and the contributions from other aberrations to the measured emittance are also analyzed in this section. Section III shows the data analysis method and the experimental results of the thermal emittance mapping. Section IV compares the thermal emittance of all beamlets with the QE, and gives the dependence of the thermal emittance on the QE for the cesium telluride photocathode.

A. beamline
The thermal emittance mapping of a cesium telluride photocathode was experimentally demonstrated at the Argonne Wakefield Accelerator (AWA) facility based on the solenoid scan method and the MLA technique. The layout of the beamline is shown in Fig. 1. An L-band 1.6-cell rf gun with a cesium telluride photocathode is illuminated by a 248 nm UV laser. The electric field on the cathode was set to 32.5 MV/m to reduce the dark current background to facilitate acquiring the low-charge bunch profile on the YAG screen. The electron beam was launched at 30 • rf phase and its energy at the gun exit was 3.2 MeV. A solenoid after the gun was used to focus the beam onto a YAG screen perpendicular to the beamline for the emittance measurement. A PI-MAX Intensified CCD (ICCD) camera [19] was used to capture beam images on the retractable YAG screen with a shutter width of 100 ns to improve the signal-to-noise ratio. The spatial resolution of the system was ∼60 µm measured with a USAF target. A calibrated strip line beam position monitor (BPM) downstream was used to measure the charge with a sensitivity of ∼40 mV/1 pC. The laser transverse modulation beamline is also present in Fig. 1. After passing through a pair of MLAs and three cylindrically-symmetric convex (focusing) lenses, the drive UV laser was redistributed to yield a pattern with two-dimensional arrays of beamlets at the location of the iris. The iris size was controlled to select a portion of the pattern and block the other beamlets. The selected seven beamlets are shown in the inset of Fig. 1. After that the pattern beam was imaged to the cesium telluride photocathode by an image transfer system consisting of a concave (defocusing) lens and a convex (focusing) lens. The laser pattern image on the virtual cathode is shown in Fig. 2, which was captured by a UV camera with high spatial resolution of 7.5 µm/pixel. Each beamlet has a Gaussian-like transverse distribution with an rms spot size of about 50 µm.  (1) (2) (5) FIG. 2. The laser transverse pattern produced by MLAs. Seven beamlets (marked as (1)- (7)) were selected and empolyed in the experiment.

B. overlap analysis
The thermal emittance can be measured by fitting the electron beam size on the YAG screen as a function of the solenoid strength. The solenoid scan range used in this study should be large enough so that the maximum beam size is about twice the minimum beam size to reduce the fitting error [20]. It is easy to achieve for a conventional solenoid scan method with large laser spot size. However, a nasty problem arises when we measure the thermal emittance map by the same solenoid scan method with a laser pattern beam. When the electron pattern beam is focused on the screen, different beamlets will overlap under some solenoid strengths, which hinders the beamsize calculation of each beamlet and deteriorates the integrity of the scanning curve. In this section, an ASTRA [21] beam dynamics simulation was performed to analyze the problem for the pattern beam. Since two beamlets are enough for the overlap analysis, an electron pattern beam with only two beamlets is employed in our simulation. Each beamlet on the cathode has a Gaussian transverse distribution (3σ cut) with an rms spot size of 50 µm. The center-to-center distance between the two beamlets is 1.812 mm, which is the same distance of two adjacent beamlets in the experiment (Fig. 2). The center of the first beamlet is at the origin of the coordinate (x=0, y=0), while the center of the second beamlet is on the x-axis with x=1.812 mm. The thermal emittances of both beamlets in the simulation are assumed to be the same, 1.05 mm mrad/mm. This is a measurement result in our previous thermal emittance measurement experiment with a large laser spot size [17].
The cathode gradient is set to 32.5 MV/m, and the laser injection phase is set to 30 • . The space charge is ex-cluded in the simulation. An overlap of the two beamlets is observed in the simulation when the solenoid strength is about 0.194 T, as shown in Fig. 3. From 0.19 T to 0.1995 T the center of the first beamlet is always at the coordinate origin, while the center of the second beamlet moves from the first quadrant to the third quadrant. In this range the two beamlets gradually merge and then gradually separate. After 0.1995 T the two beamlets are completely separated, making it possible to calculate the transverse beamsize of each beamlet. The rms beamsize of each beamlet as a function of the solenoid strength after 0.2 T is calculated in the simulation, shown as the red stars in Fig. 4(a). We found that the beamlet beamsize after the overlap first becomes smaller and then becomes larger as the solenoid strength increases. The center-to-center distance of the two beamlets, shown as the red stars in Fig. 4(b), monotonically increases with the increase of the solenoid strength, which means no beamlet overlap in the solenoid scan range. Based on our simulation, the waist of the beamlet beamsize in the solenoid scan range is at about 0.222 T, while the beamlets overlap at 0.194 T. The difference of the solenoid strength corresponding to the waist and the overlap situation indicates that we can collect a complete scan curve without the bother of the overlap problem.
A matrix calculation method is employed to analyze this phenomenon. In a transverse Larmor coordinate, i.e., the axis rotates along the rotation angle in the solenoid, the motion of an electron can be expressed as a matrix form: where x 0 is the initial position on the cathode, x is the final position on the screen. p x = β x γ is the normalized momentum. R ij is the element of the transfer matrix from the cathode to the screen in the Larmor coordinates. Based on Eqn. (1) the final position x is written as The center of an electron beam should be the average of all electrons, i.e.,x = R 11x0 + R 12px0 .p x0 should be 0 because the initial emission on the cathode is considered to be isotropic. Therefore, the center of the beam on the screen should bex The rms beamsize square of the electron beam can be expressed as . The x 0 p x0 term should be 0 because an isotropic emission on the cathode suggests no coupling of x 0 and p x0 . Therefore, the rms beamsize square on the screen should be The transfer matrix from the cathode to the screen can be calculated by Eqn. (5) and Eqn. (6), which considers the field in the gun and in the solenoid simultaneously [22].
where C ≡ cos[∆θ L (z)], S ≡ sin[∆θ L (z)]. ∆θ L (z) is the rotation angle in a time step. b is the normalized solenoid field defined as b = −e B z /2mc. p i and p f are the initial and final normalized momentum in the time step respectively. The distance between the cathode to the screen is divided into numerous time steps. ∆R i x,px is a submatrix at the time t i with a time step of ∆t. The total transfer matrix R is the product of all submatrix ∆R i x,px in the order from the screen to the cathode.
The real on-axis fields in the gun and the solenoid are used in the matrix calculation based on Eqn. (5)- (7). The cathode gradient is set to 32.5 MV/m, and the laser injection phase is set to 30 • . The matrix elements R 11 and R 12 as a function of the solenoid strength are present in Fig. 5. For the aforementioned ASTRA simulation, the center position of the first beamlet on the screen is always 0 sincex 0 = 0. The center position of the second beamlet x is a function of R 11 based on Eqn. (3) with a constantx 0 of 1.812 mm. Therefore, the distance of the two beamlets should be the absolute value of the center position of the second beamlet |x|. When R 11 = 0, the distance of the two beamlets is zero, indicating an overlap of the two beamlets. We found from Fig. 5(a) that the solenoid strength is 0.194 T when R 11 = 0 (beamlets overlap). This is in good agreement with the simulation result shown in Fig. 3.
Moreover, x 2 0 and p 2 x0 in Eqn. (4) denote the beamlet beamsize square and the thermal emittance square on the cathode respectively. By substituting R 11 and R 12 shown in Fig. 5 into Eqn. (3) and Eqn. (4), the distance of the two beamlets and the beamlet beamsize are calculated as a function of the solenoid strength, shown as the solid blue lines in Fig. 4(b) and (a) respectively, which is also in good agreement with the ASTRA simulation.

C. error analysis
The measured emittance is the quadrature sum of the thermal emittance and the emittance contributions due to various aberrations in the beamline: ε measured = ε therm 2 +ε other 2 (8) where ǫ other is the emittance growth due to other mechanisms such as space charge [23], rf field [24], spherical/chromatic aberrations [25,26], and coupled aberrations [17,27]. The beam parameters were optimized to minimize ε other in the experiment in order to reduce the measurement error of the thermal emittance. The space charge effect was minimized during the experiment by using a low-charge beam. The charge was gradually reduced until the measured emittance did not change, and the details will be present in Section III. The following aberrations were minimized via ASTRA simulations. A 3D field map in the gun exported from CST [28] was used to simulate the rf contributions. The solenoid strength was adjusted to focus the beam on the screen, so that the spherical/chromatic contributions from the solenoid were included. Our previous work [17] shows that a quadrupole with strength of 77 Gauss/m (0.1974 T) and rotation angle of 12 • exists in the solenoid, and this is also included in our simulation to consider the coupled aberrations. The initial beam has a transversely Gaussian distribution (3σ cut) with an rms spot size of 50 µm, and a longitudinally Gaussian distribution (3σ cut) with an FWHM duration of 1.5 ps. Beamlet No. (3) is assumed to be at the center of the cathode. The center of the Beamlets No. (1)(2)(4)(6) has an offset of 1.812 mm to the cathode center, while the center of the Beamlets No. (5)(7) has an offset of 2.563 mm to the cathode center. Therefore, the initial beamlets with three kinds of offset, 2.563 mm, 1.812 mm and 0 mm, were simulated in our simulation, showing that the emittance growth due to other aberrations is only 0.4%, 0.3% and 0.2% for the offset of 2.563 mm, 1.812 mm and 0 mm respectively. Therefore, the total contribution to the measured emittance from other sources is very small and is neglected in the study.

III. THERMAL EMITTANCE MAPPING WITH SOLENOID SCAN
During the experiment the cathode gradient was 32.5 MV/m, and the laser injection phase was 30 • . The laser Beamlet No. (3) was kept on the center of the cathode, so the position of the electron Beamlet No. (3) on the screen didn't change with the change of the solenoid strength. The solenoid strength was scanned and the images of the electron pattern beam were monitored by the ICCD camera. All beamlets overlapped when the solenoid strength was about 0.194 T, which is consistent with the expectations based on our simulation and matrix calculation. With the further increase of the solenoid strength, all beamlets started to separate. The pattern images after complete separation with the increase of the solenoid strength are plotted in Fig. 6. As predicted by the simulation and the matrix calculations, the distance of all beamlets increases with the increase of the solenoid strength. The distance is large enough to calculate the spot size of each beamlet after 0.2045 T. The spot size of each beamlet becomes smaller and then becomes larger with the increase of the solenoid strength.
Background images without the laser injection were captured before the collection of the electron pattern images. The background was subtracted from each beam image to reduce the dark current noise. Each beamlet was manually selected and the beamlet image was projected to x and y directions. A Gaussian fitting was employed to roughly calculate the center of the beamlet and the beamsizes σ gx and σ gy . A circle was drawn on the image with the center at the beamlet center, and with the radius of 3 √ σ gx σ gy . The pixels inside the circle were preserved and the pixels outside the circle were set to zero. Then the image was projected to x and y directions again, and an rms method with a 95% area cut [15,29] was used to calculate the rms beamsize. The geometric average of the rms beamsizes in x and y directions, σ = √ σ x σ y , was used for the emittance fitting.
The rms beamsize at each solenoid strength was averaged with 6 images to reduce the impact of beamsize fluctuation on the curve fitting. The rms beamsize σ of all seven beamlets as a function of the solenoid strength is shown in Fig. 7. The red solid curves are the fitting results of the measured emittance.
The space charge contribution to the measured emittance was minimized by gradually reducing the total charge of the pattern beam. Neutral density filters with different transmittance were used on the laser beamline to change the pulse energy of the laser pattern beam, so as to change the bunch charge of the electron pattern beam. The bunch charge of every beamlet can be calculated by distributing the total charge of the electron pattern beam according to the relative intensity of the beamlet on the image. As an example, the measured emittance of the beamlet No. (1) as a function of the beamlet charge is shown in Fig. 8. The difference of the measured emittance is submerged within the measurement error when the beamlet charge is less than 20 fC. The measurement results shown in Fig. 7 and following are all obtained with the beamlet charge less than 20 fC, and the space charge contribution to the measured emittance is negligible.
The measurement results of the thermal emittance for the seven beamlets are summarized as Table I. The beamsize calculation method of the laser beamlets are the same as the electron beamlets, and the rms spot size of all seven beamlets σ laser , are present in the table. The thermal emittance ǫ/σ laser is the measured emittance ǫ over the laser spot size. Our previous thermal emittance measurement [17] using a homogenized laser beam with 3 mm diameter shows that the thermal emittance is 1.05 mm mrad/mm, i.e., the average value of the thermal emittance in the laser injection area is 1.05 mm mrad/mm. In this experiment, the thermal emittances of the seven beamlets vary from 0.934 mm mrad/mm to 1.142 mm mrad/mm, which are close to the average of the thermal emittance.

IV. THERMAL EMITTANCE VS. QE
The laser pattern beam produced by MLAs can also be used to measure the quantum efficiency (QE) map [30]. The charge of each beamlet was calculated by distribut- ing the total charge of the electron pattern beam according to the relative intensity of the beamlets on the YAG screen. Similarly, the laser energy of each beamlet can also be calculated by distributing the total pulse energy of the laser pattern beam according to the relative intensity of the beamlets on the virtual cathode. The QE of each beamlet was calculated by the ratio of the number of the emitted electrons (bunch charge) to the incident photons (laser pulse energy).
The measured thermal emittance ǫ/σ laser and the QE of the seven beamlets are plotted in Fig. 9. Generally, we found that the beamlets with higher QE also have a higher thermal emittance.
Based on the conventional theory of three-step model, the thermal emittance should be proportional to the square root of the excess energy [31], i.e., ε/σ laser ∝ hν − φ ef f , where hν − φ ef f is the excess energy. Besides, the QE should be proportional to the square of the excess energy [32], i.e., QE ∝ (hν − φ ef f ) 2 . As a result, the relation of the thermal emittance and the QE can be  (2) (1) (4) (7) FIG. 9. The black circles are the measured thermal emittance ǫ/σ laser and the QE of the seven beamlets. The beamlets numbers (1)-(7) are present. A fitting of the thermal emittance and QE is shown as the green line based on the function ǫ/σ laser = a × 4 √ QE and giving a=2.067.
expressed as where a is a constant. A least-square fitting of thermal emittance and QE of the seven beamlets based on Eqn. (9) is shown as the green line in Fig. 9, indicating that the fitting factor a for the cesium telluride cathode is 2.067.

V. CONCLUSION
In conclusion, the thermal emittance map of the cesium telluride photocathode was measured by the solenoidscan method. A pair of MLAs were employed to produce a periodic transverse pattern beam, consisting of a twodimensional array of laser beamlets. Every laser beamlet has an rms spot size of about 50µm. The laser pattern beam was illuminated onto the cesium telluride cathode to produce an electron pattern beam. The rms beamsize of the electron beamlets was measured on a YAG screen with different solenoid strengths. An ASTRA simulation and a matrix calculation show that the electron beamlet will not overlap in the solenoid scan range, making it possible to obtain a complete scan curve with the rms beamsize first becomes smaller and then becomes larger. The experimental results are consistent with the expectations from the ASTRA simulation and the matrix calculation. The measured thermal emittances of the seven beamlets vary from 0.934 mm mrad/mm to 1.142 mm mrad/mm, which are close to the average of the thermal emittance in the laser injection area with 3 mm diameter. The quantum efficiency map was also measured by the pattern beam, and the thermal emittance and the QE of the beamlets are compared. Finally, the dependence of the thermal emittance on the QE for the cesium telluride photocathode is present.